Linear networks, or nonlinear networks operating with signals sufficiently small to cause the networks to respond in a linear manner, can be completely characterized by parameters measured at the network terminals (ports) without regard to the contents of the networks. Once the parameters of a network have been determined, its behavior in any external environment can be predicted, again without regard to the contents of the network.
Although a network may have any number of ports, network parameters can be explained most easily by considering a network with only two ports, an input port and an output port, like the network shown in FIG. 1.
To characterize the performance of such a network, any of several parameter sets can be used, each of which has certain advantages. Each parameter set is related to a set of four variables associated with the two-port model. Two of these variables represent the excitation of the network (independent variables), and the remaining two represent the response of the network to the excitation (dependent variables). If the network in FIG. 1 is excited by voltage sources V1 and V2, the network currents I1 and I2 will be related by any of the following equations:
H-ParametersY-ParametersZ-ParametersV1 = h11I1 + h12V2I1 = y11V1 + y12V2V1 = z11I1 + z12I2I2 = h21I1 + h22V2I2 = y21V1 + y22V2V2 = z21I1 + z22I2
The only difference in the parameter sets is the choice of independent and dependent variables. The parameters are the constants used to relate these variables.
The above H-parameters can be used as an explanatory example to clarify how parameter sets of this type can be determined through measurement. The parameter h11 is determined by setting V2 equal to zero, e.g. by applying a short circuit to the output port of the network. The parameter h11 is then the ratio of V1 to I1, I.e. the input impedance of the resulting network. The parameter h12 is in turn determined by measuring the ratio of V1 to V2 (I.e. the reverse voltage gain) having the input port open circuited. It is important to note that both open and short circuits are essential for obtaining the above-mentioned H-parameters, Y-parameters and Z-parameters.
However, the use of said H-, Y- and Z-parameters in connection with higher frequencies, especially in the microwave domain, present a problem since a short circuit looks like an inductor and an open circuit has some leakage capacitance. Active devices such as transistors and tunnel diodes are often instable if short or open circuited. In addition it is difficult to achieve short and open circuits over a broad band of frequencies, which is typically required. Moreover, it is difficult to measure total current or total voltage, which is required when using H-, Y-, or Z-parameters.
It is obvious that another method has to be used for characterizing these devices at high frequencies, especially microwave frequencies.
If we embed the exemplifying two-port device in FIG. 1 into a transmission line, and terminate the transmission line in its characteristic impedance ZL, we can think of the stimulus signal provided by a generator having a impedance ZS that matches said characteristic impedance as a traveling wave incident on the device, and the response signal as a wave reflecting from the device or being transmitted through the device, see FIG. 2.
We can then establish this new set of equations relating these incident and “scattered” waves:E1r=S11E1i+S12E2i  [1]E2r=S21E1i+S22E2i  [2]Wherein E1r and E2r are the dependent voltages reflected from the 1st and 2nd ports respectively, whereas E1i and E2i are the independent voltages incident upon the 1st and 2nd ports respectively.
Dividing the new set of equations by Z0 (where Z0 is the characteristic impedance of the transmission line) we can alter these equations to a more recognizable form:b1=S11a1+S12a2  [3]b2=S21a1+S22a2  [4]Wherein
                                              ⁢                                            b              n                        =                                          E                nr                                                              Z                  0                                                              ,                                          ⁢          and                ⁢                                                      [        5        ]                                                      a            n                    =                                    E              ni                                                      Z                0                                                    ;                            [        6        ]            and wherein:    S11 is the input reflection coefficient equal to b1/a1 with a2=0, i.e. no incident wave E2i, which is accomplished by terminating the output of the two-port in an impedance equal to Z0.    S22 is the output reflection coefficient equal to b2/a2 with a1=0, I.e. no incident wave E1i, which is accomplished by terminating the input of the two-port in an impedance equal to Z0.    S21 is the forward transmission (insertion) gain equal to b2/a1 with a2=0, I.e. no incident wave E2i, which is accomplished by terminating the output of the two-port in an impedance equal to Z0.    S12 is the reverse transmission (insertion) gain equal to b1/a2 with a1=0, i.e. no incident wave E1i, which is accomplished by terminating the input of the two-port in an impedance equal to Z0.
Where, for example:
|b1|2=Power reflected from the 1st port; and
|a1|2=Power incident on the 1st port.
The above scattering parameters or S-parameters are determined with resistive termination, which obviates the difficulties involved in obtaining the broadband open and short circuit conditions required for the H-, Y-, and Z-parameters. Moreover, parasitic oscillations in active devices are minimized when the device is terminated in resistive loads. There is also standard equipment available for determining S-parameters since only incident wave Eni and reflected voltages need to be measured.
S-parameters are conveniently measured by means of modern professional microwave network analyzers, e.g. the Agilent E8362B vector network analyzer from Agilent Technologies Inc. with Head Quarters in Palo Alto, Calif., USA. S-parameters are measured by a modern microwave network analyzer substantially in the same way as indicated above, I.e. by providing a well-defined incident wave E1i, E2i to the device under test and by measuring a possible reflected wave E1r, E2r caused by the incident wave E1i, E2i. The conventional way to do this is to provide an incident wave E1i, E2i with a frequency sweep that covers all the frequencies of interest for a certain state of a device under test, and then change the state of the device under test and provide a new frequency sweep.
However, the number of states that need to be measured tends to be very large when measuring a device that can assume several thousand of different states. An example of such a device is the transmit-and-receive modules (T/R-module) in radar equipments. Such T/R-modules can assume thousands of different states regarding phase and magnitude. Each such state affects the magnitude and/or phase of a signal that is transmitted or a signal that is received by the T/R-module.
The states in a T/R-module or a similar device under test can be changed very fast compared to changing the frequency in a network analyzer to accomplish a frequency sweep. Typically it takes milliseconds to change the frequency in a network analyzer and just 20-30 μs to change the state in the T/R-modules that are commonly measured today.
Moreover, it takes time to extract measured data from the microwave network analyzer to an external verification unit in setups comprising a verification unit. Every time communication is established there is also a certain amount of overhead. Depending on the type of instrument and the protocol used the total time for extracting data varies. In the Agilent E8362B the time is typically 30-100 milliseconds.
The time consumed during frequency change (10-20 ms for each frequency) and data retrieving with a microwave network analyzer (30-100 ms) is multiplied with the number of states that are to be measured. If a lot of states are to be measured this easily takes hours, e.g. when characterizing a T/R-module that may assume more than 600000 states. Such delays are clearly an inconvenience, particularly if a large number of T/R-modules or similar devices are to be characterized, which e.g. may be the case when developing and manufacturing such modules.
Consequently, there is a need for a method that gives a much faster measurement.